The job criteria for the incoming chairman of the BBC Trust has been quietly changed amid suggestions the Government’s preferred choice Sebastian Coe is too busy to commit to a four-day-a-week role.

The Conservative peer and leader of the London Olympic Games’ organising committee has won support from David Cameron and Boris Johnson in the race to replace Lord Patten as the high-profile head of the BBC’s governing body.

However Lord Coe, a former judo partner of Foreign Secretary William Hague, has a number of outside business interests including commitments to Chime Communications, which bought his sports-marketing and image-rights business last year.

When the position was advertised on the Cabinet Office website earlier this month, the “time requirements” stated the need to work “3-4 days per week (or 12-16 days per month)”.

However, earlier this week officials at the Department for Culture, Media and Sport (DCMS) updated the job description to add the phrase: “Suitable candidates able to offer a lesser time commitment will also be considered.”

The tweak to the job criteria appears designed to clear the way for a truly part-time candidate with major outside commitments – raising fears they may be unable to devote sufficient attention to the role.

The incumbent Lord Patten, who announced he was stepping down following heart surgery, worked a four-day week as chairman of the BBC Trust – described recently as a “high-profile, high-wire job where the slightest slip can make front-page news”.

Lord Coe sold Complete Leisure Group (CLG), to Chime in January 2013 and has been working there four-days-a-week. Coe’s CLG got £1.8m in remuneration last year and is in line for an “earn-out” that could be worth £10.2m if he stays until 2017, raising questions over whether he could juggle the commercial role with the BBC Trust job, which pays £110,000 a year.

Lord Coe has previously admitted he was thinking about applying to replace Lord Patten, the last governor of Hong Kong. “It is a very meaty job and I’m passionate about public service broadcasting,” he told the BBC. “But the honest answer is I probably have a few weeks to think about it.”

The former Olympic gold medallist, who won widespread acclaim for his handling of the 2012 London Games, did not deny he had been contacted by Tory members of the Coalition, but said no formal approach had been made.

Earlier this month, London Mayor Boris Johnson was effusive in his praise of Lord Coe, and said he would be a “first-rate choice” to head the BBC Trust. “I think it’s fantastic news for the BBC and British broadcasting,” said Johnson. “Seb Coe is a great leader. I’ve worked with him a lot over the past few years and I think he’ll demand very high standards of the BBC... he’ll be exactly in the right tradition of British broadcasting.”

Another possible obstacle is Lord Coe’s interest in the world of international sport politics. Following his success at the London Olympics, he is also said to be considering a tilt for the presidency of the International Association of Athletics Federations (IAAF) which could lead to the ultimate prize: heading up the International Olympic Committee.

A DCMS spokesperson said: “We will consider any suitable candidates who can commit to less than 3-4 days a week. It is essential we appoint the best possible person to the position so we must ensure we have the widest possible field of candidates.”